Question

The position of a particle is given by the expression x = 2.00 cos (2.00πt + 2π/5), where x is in meters and t is in seconds.

a) Determine the frequency
b) determine the period of motion
c) determine amplitude of motion
d) determine phase constant
e) determine position of particle at t = 0.310

Answer 1

The equation in which a particle undergoes SHM (Simple Harmonic Motion) is:

Where A is the amplidude is the angular frequency and is the phase constant

x = 2.00 cos (2.00πt + 2π/5)

Therefore,

Angular Frequency: 2π

Phase Constant: 2π/5 (which already answers part e for you)

Amplitude: 2.00 (which already answers part c for you)

A. To find the frequency:

= 2πf

ω/2π = f

ω = 2π

So, f = 2π/2π = 1hz (hz = hertz)

B. To find the period:

Since we have the frequency and it's one, the period of motion would be 1s (s = seconds)

e. To find the position of the particle, we'll just plug and chug this since we already have what we need:

=

=

=

So the answer is: